The 25-year-old striker arrives from the Serie A side on a season-long deal, subject to a work permit, with the option of a permanent switch at the end of the campaign.
N'Diaye has also had spells with Italian clubs Verona, AC Cesana, Genoa and Lecce and was in the Senegal squad for the 2008 African Cup of Nations.
Boss Alan Pardew said: "We wanted another creative player and he comes highly recommended.
"He's a quick, creative forward player who will help us score more goals and I can't wait to see him in a Saints shirt."
N'Diaye added: "I am excited to be coming to England and I'm looking forward to showing the Southampton fans what I can do."